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    Semiregular trees with minimal Laplacian spectral radius
    (Elsevier Inc, 2010-04-15) Bıyıkoğlu, Türker; Leydold, Josef
    A semiregular tree is a tree where all non-pendant vertices have the same degree. Among all semiregular trees with fixed order and degree, a graph with minimal (adjacency/Laplacian) spectral radius is a caterpillar. Counter examples show that the result cannot be generalized to the class of trees with a given (non-constant) degree sequence.